What is the integral of integral of e^{-(x^2+4y^2)} ?

The integral of integral of e^{-(x^2+4y^2)} is Cx+Ae^{-4y^2}(sqrt(pi))/2 \erf(x)+C

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integral of integral of e^{-(x^2+4y^2)}

\int \int e^{- (x^{2} + 4 y^{2})} d A

C x + A e^{- 4 y^{2}} \frac{π}{2} erf (x) + C

Solution steps

\int \int e^{- (x^{2} + 4 y^{2})} d A

\int e^{- (x^{2} + 4 y^{2})} d A = e^{- x^{2} - 4 y^{2}} A + C

= \int (e^{- x^{2} - 4 y^{2}} A + C)

\int (e^{- x^{2} - 4 y^{2}} A + C) d x = C x + A e^{- 4 y^{2}} \frac{π}{2} erf (x) + C

= C x + A e^{- 4 y^{2}} \frac{π}{2} erf (x) + C

What is the integral of integral of e^{-(x^2+4y^2)} ?
The integral of integral of e^{-(x^2+4y^2)} is Cx+Ae^{-4y^2}(sqrt(pi))/2 \erf(x)+C